Question

ayuda ayudaaaaaaaaaaaa​

Answer 1

Respuesta:

Explicación paso a paso:

1) $\sqrt{2(3)^{2}(5)^{5} } = \sqrt{2(3)^{2}(5)^{2} (5)^{2}(5)^{1} } = 3*5*5\sqrt{2*5} = 75\sqrt{10}$

2)

$\sqrt[4]{2^{7}*3^{14}*5^{4} } = \sqrt[4]{2^{4}*2^{3}*3^{4}*3^{4}*3^{4}*3^{2}*5^{4} } }\\\\ = 2*3*3*3*5\sqrt{2^{3}*3^{2} } \\\\= 270\sqrt[4]{8*9} \\\\= 270\sqrt[4]{72}$

3) $\sqrt[3]{81a^{3}b^{5} c } = \sqrt[3]{3^{3}*3^{1} *a^{3}*b^{3}*b^{2}* c } = 3ab\sqrt[3]{3b^{2} c}$

4)

$\sqrt[3]{54} - \sqrt[3]{16} + \sqrt[3]{250} \\\\\sqrt[3]{27*2} - \sqrt[3]{8*2} + \sqrt[3]{125*2} \\\\\sqrt[3]{3^{3}*2 } - \sqrt[3]{2^{3}*2 } + \sqrt[3]{5^{3}*2 } = 3\sqrt[3]{2} - 2\sqrt[3]{2} + 5\sqrt[3]{2} = 6\sqrt[3]{2}$

5) $\sqrt{2} + \frac{1}{\sqrt{2} } = \frac{\sqrt{2}*\sqrt{2}+1 }{\sqrt{2} } = \frac{2+1}{\sqrt{2} }= \frac{3}{\sqrt{2} }*\frac{\sqrt{2} }{\sqrt{2} } = \frac{3\sqrt{2} }{\sqrt{2}*\sqrt{2} }= \frac{3\sqrt{2} }{2}$  

6) $\sqrt{2} *\sqrt{6} = \sqrt{12} = \sqrt{4*3} = \sqrt{2^{2}*3 } = 2\sqrt{3}$

7) $\sqrt{3} * \sqrt[3]{9} *\sqrt[4]{27} = \sqrt[2]{3} * \sqrt[3]{3^{2} } * \sqrt[4]{3^{3} } = \sqrt[(2*3*4)]{3^{(1*2*3)} } = \sqrt[24]{3^{6} } = \sqrt[4]{3}$

8) $\sqrt{12} * \sqrt[3]{36} = \sqrt[2]{4^{1}*3^{1} } * \sqrt[3]{4^{1}*3^{2} } = \sqrt[(3*2)]{4^{(1+1)}*3^{(1+2)} } = \sqrt[6]{4^{2} *3^{3} }$

    $= \sqrt[6]{4^{2} } * \sqrt[6]{3^{3} } = \sqrt[3]{4} *\sqrt{3}$

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